Expected disk wind properties evolution along an X-ray Binary outburst
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Astronomy & Astrophysics manuscript no. 39524newb ©ESO 2021
March 11, 2021
Expected disk wind properties evolution along an X-ray Binary
outburst
P.-O. Petrucci1 , S. Bianchi2 , G. Ponti3 , J. Ferreira1 , G. Marcel4 , F. Cangemi5 , S. Chakravorty6 , M. Clavel1 , J. Malzac7 ,
J. Rodriguez5 , S. Barnier1 , R. Belmont5 , S. Corbel5 , M. Coriat7 , and G. Henri1
1
Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
2
Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, via della Vasca Navale 84, 00146 Roma, Italy
3
INAF-Osservatorio Astronomico di Brera, Via Bianchi 46, 23807 Merate, LC, Italy
4
Villanova University, Department of Physics, Villanova, PA 19085, USA
5
arXiv:2103.04601v2 [astro-ph.HE] 10 Mar 2021
AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, F-91191 Gif-sur-Yvette, France
6
Department of Physics, Indian Institute of Science, Bangalore 560012, India
7
IRAP, Université de toulouse, CNRS, UPS, CNES , Toulouse, France
Received .../Accepted ...
ABSTRACT
Blueshifted X-ray absorption lines (preferentially from Fe XXV and Fe XXVI present in the 6–8 keV range) indicating the presence
of massive hot disk winds in Black Hole (BH) X-ray binaries (XrB) are most generally observed during the soft states. It has been
recently suggested that the non-detection of such hot wind signatures in the hard states could be due to the thermal instability of
the wind in the ionization domain consistent with Fe XXV and Fe XXVI. Studying the wind thermal stability requires however a
very good knowledge of the spectral shape of the ionizing Spectral Energy Distribution (SED). We discuss in this paper the expected
evolution of the disk wind properties during an entire outburst by using the RXTE observations of GX 339-4 during its 2010–2011
outburst. While GX 339-4 never showed signatures of a hot wind in the X-rays, the dataset used is optimal to illustrate our purposes.
We compute the corresponding stability curves of the wind using the SED obtained with the Jet-Emitting Disk model. We show that
the disk wind can transit from stable to unstable states for Fe XXV and Fe XXVI ions on a day time scale. While the absence of wind
absorption features in hard states could be explained by this instability, their presence in soft states seems to require changes of the
wind properties (e.g. density) during the spectral transitions between hard and soft states. We propose that these changes could be
partly due to the variation of heating power release at the accretion disk surface through irradiation by the central X-ray source. The
evolution of the disk wind properties discussed in this paper could be confirmed through the daily monitoring of the spectral transition
of a high-inclination BH XrB.
1. Introduction & McClintock 2006 or Done et al. 2007 for reviews). At the
beginning and end of the outburst, the system is in the so-called
Low mass X-ray binaries (XrB) are binary systems containing hard state. During this state, the X-ray spectrum has a hard
a main sequence star and a compact object (neutron star or power-law shape up to few tens of keV, signature of non-thermal
black hole). Due to Roche lobe overflow, the matter is pulled off processes in a very hot, optically thin, plasma (the so-called
from the star and forms an accretion disk around the compact corona). The radio emission observed in this state, that extends
object (see Tauris & van den Heuvel 2006 for a review). XrBs up to the Infrared (IR), is believed to be entirely produced by
spend most of their time in a quiescent state at very low mass a steady jet. During the middle part of the outburst, the system
accretion rates. Occasionally, they come out of the quiescent is in the so-called soft state where the spectrum is dominated
state and undergo outbursts that last from a few months to a year, by a bump in the soft X-rays (< 2 keV) commonly interpreted
during which their flux rises by several orders of magnitude as the thermal emission from the inner region (close to the
across the whole electromagnetic spectrum (e.g. Remillard innermost stable circular orbit, hereafter ISCO) of an optically
& McClintock 2006). This release of gravitational power is thick accretion disk. In this state, the radio/IR emission is
believed to result from disk instabilities in the outer part of the strongly reduced (e.g. Coriat et al. 2009) and even undetectable
accretion flow, driven by the ionization of hydrogen above a in most cases, suggesting the disappearance (or strong fading)
critical temperature (e.g. Meyer & Meyer-Hofmeister 1981; of the jet component. In between these two main states, the
Smak 1984 and Hameury 2020 for a recent review). system transitions, in a few days, through the so-called (hard
and soft) intermediate states. The spectral shape evolves from
During the outburst, XrBs exhibit a large panel of spectral hard-to-soft, in the first part of the outburst, and then from
and timing properties. Black hole (BH) XrB (which are the soft-to-hard, at the end of the outburst before turning back to the
one we are interested in this paper and labeled BH XrB or quiescent state (e.g. Remillard & McClintock 2006; Done et al.
simply XrB in the following) can be easily distinguished in the 2007).
so-called Hardness-Intensity Diagram (HID) where the X-ray
luminosity is plotted against the hardness ratio of the X-ray
spectrum, producing a hysteresis with a typical Q-shaped track. In the last 15 years it has been realized that, while soft
All BH XrBs generally follow the same spectral evolution (e.g. states do not show signatures of jet, the presence of blue shifted
Homan & Belloni 2005; Dunn et al. 2010, and see Remillard absorption lines, generally from Fe XXV and Fe XXVI, indi-
Article number, page 1 of 14
A&A proofs: manuscript no. 39524newb
cates the existence of massive hot disk winds (see Díaz Trigo & & Muñoz-Darias 2020), but will be detectable only in the soft
Boirin (2016) and Ponti et al. (2016) for recent reviews). While state, when the relevant (for Fe XXV and Fe XXVI) range of
not detected in the hard states, these winds are generally present ionization parameter corresponds to stable thermal equilibrium.
in the soft states of inclined systems (e.g. Ponti et al. 2012). But
the picture is certainly more complicated than a simple on-off Stability curves are very useful to study more precisely
wind process between spectral states (e.g. Muñoz-Darias et al. the role of the thermal stability on the wind properties. They
2016; Homan et al. 2016; Sánchez-Sierras & Muñoz-Darias represent the photoionization equilibrium states of a plasma
2020), and recent results during the (hard and soft) intermediate illuminated by a broad band Spectral Energy Distribution
states show a large variety of wind properties and signatures (SED). The computation of these stability curves is however
(Miller et al. 2008b; Kallman et al. 2009; Rahoui et al. 2014; very sensitive to the spectral shape of the illuminating SED (e.g.
Neilsen et al. 2016; Shidatsu et al. 2016; Muñoz-Darias et al. Chakravorty et al. 2013; Bianchi et al. 2017). The precise study
2017; Mata Sánchez et al. 2018; Gatuzz et al. 2019). The of the wind thermal stability during an outburst, and especially
physical processes at the origin of these disk winds are not during the spectral transitions, then requires the knowledge of
completely understood but observations favored thermal or the spectrum in the broadest energy range possible. However,
magnetic driving (or a combination of the two) as the most Galactic hydrogen absorbs the soft X-rays (< 0.1 keV) and
probable launching mechanisms (e.g. Díaz Trigo & Boirin instrumental limitations prevent access to a precise spectra
2016; Tetarenko et al. 2018b). The dependence of the wind for hard X-rays (> 50 keV). With the typical 0.5-10 keV
detection with the spectral state of the X-ray source is however energy range (from e.g. Chandra or XMM), extrapolating
not straightforward. Indeed, assuming that the outflow velocity from phenomenological models is hazardous and could lead
is of the order of the escape velocity of the absorbing material, to unphysical broad band spectral shapes and, consequently,
the observed blue-shifts generally put the absorbing wind at up erroneous stability curves. With the lack of daily broad band
to few/hundreds of thousand of gravitational radii away from the monitoring of XrB, the best alternative is the use of physically
X-ray emitting region located close to the black hole (Schulz & motivated models to obtain reasonable extrapolations where the
Brandt 2002; Ueda et al. 2004; Kubota et al. 2007; Miller et al. data are missing.
2008a; Kallman et al. 2009). In XrBs, such distances correspond
to the outer part of the accretion disk. This connection between This is the purpose of the present paper. We discuss the
the inner and outer part of the accretion flow cannot occur on expected evolution of the disk wind properties of an XrB by
accretion (i.e. viscous) timescale since it is expected to be of using the detailed observations of the most famous (and thus
the order of several weeks to months, i.e. the typical duration best monitored) one i.e. GX 339-4. No wind signature has been
of the observed outbursts1 . This is much longer than the few detected in this object potentially due to the low inclination of
days duration for a typical transition between a hard (windless) our line-of-sight (Ponti et al. 2012, but see Miller et al. 2015 for
state to a soft (windy) state (e.g. Dunn et al. 2010). To explain the marginal detection of He-like Fe XXV and H-like Fe XXVI
the observations, the communication between the X-ray corona emission lines during a high/soft state of this source, potential
and the wind must therefore be much faster than the accretion signatures of a wind). Even if GX 339-4 is not the prototype
time scale. It has been pointed out that over-ionization, as a of a windy XrB, we believe that its spectral behavior along an
consequence of the much harder illuminating spectral energy outburst can be used, as representative, to trace the one followed
distribution during hard states might play a role (see e.g. by any XrB. In consequence, its SED can be used to trace the
Shidatsu & Done 2019) but in several instances it may not be expected evolution of the stability curve of a windy source. GX
sufficient (e.g. Neilsen & Homan 2012; Ponti et al. 2015) 339-4 entered several times in outburst in the last 20 years and
for which a large amount of data exist (see e.g. the WATCH-
It has been recently understood that the spectral state of the DOG all-sky database Tetarenko et al. 2016). Its 2010–2011
central source has a huge impact on the thermal stability of the outburst for example was very well followed in X-rays and
wind and its ionization state (Chakravorty et al. 2013, 2016; radio. It was observed by RXTE for more than 400 days with
Bianchi et al. 2017; Higginbottom et al. 2020). When illumi- almost one observation every day. Marcel et al. (2019) recently
nated by a soft state spectrum, the wind is always thermally reproduced the spectral shapes of each observation during the
stable regardless of its ionization parameter. When the spectrum entire outburst with the Jet Emitting Disk (JED) model (Ferreira
is hard, however, large parts of the stability curve are thermally et al. 2006; Marcel et al. 2018b,a). The corresponding best-fit
unstable, in particular in the ionization domain required for SEDs are well constrained by the RXTE/PCA observations.
the production of Fe XXV and Fe XXVI ions. The timescale While model dependent, they are however physically motivated
for the thermal instability to take place depends on the cooling and give consistent extrapolations outside the energy window of
timescale of the gas and, for the expected wind density (see Sect. RXTE. We thus make the choice to use these SEDs to compute
2), is quite fast (< day, see e.g. Gonçalves et al. 2007; Bianchi the wind stability curves and follow their evolution day by day,
et al. 2017). These arguments support the importance of the keeping in mind however their model-dependency. Assuming
thermal instability process in the changes of the wind ionization GX 339-4 is a typical XrB, this evolution of the stability curves
state (but see Sect. 2.2 for potential caveats). In this context, the is expected to be quite generic for all XrBs. Moreover, the very
disk wind could be present at all times (as recently suggested by good sampling of the hard-to-soft transition of the 2010-2011
the observation of near-IR emission lines all along the outburst outburst of GX 339-4 is optimal to illustrate our purposes. None
of the black hole transient MAXI J1820+070, Sánchez-Sierras of the sources which show absorption lines in its spectra have as
extensive coverage of SEDs as a function of state evolution.
1
For an α-disk (Shakura & Sunyaev 1973) around a 10 solar-mass
black hole characterized by a disk aspect ratio H/R, with H the height
of the disk at the radius R = rRg , the accretion timescale to reach the This paper is organized as follows. In Sec. 2 we explain how
black hole from the disk radius R is tvisc = 5 × 10−5 (H/R)−2 α−1 r3/2 we compute the stability curves. Then, we present and discuss
seconds. For H/R = 10−2 , α = 0.1 and R = 104 Rg , tvisc ' 60 days. It in details their evolution all along the outburst in Sec. 3. Our
becomes ∼ 2000 days for R = 105 Rg . results suggest significant changes in the disk wind properties
Article number, page 2 of 14
P.-O. Petrucci et al.: Expected disk wind properties evolution along an X-ray Binary outburst
during the state transitions, discussed in Sec. 4. We propose that MJD Rtr Ṁ L1−1000Ry L1−100keV Lbol
the disk illumination plays a major role in the wind observable (Rg ) ( ṀEdd ) (LEdd ) (LEdd ) (LEdd )
properties. We conclude in Sect. 5. 55208 27.1 0.63 0.019 0.014 0.043
55271 23.1 1.57 0.062 0.083 0.174
55293 23.1 2.42 0.094 0.130 0.248
55294 21.6 2.42 0.099 0.132 0.249
2. Stability curves computation 55295 9.6 2.34 0.177 0.157 0.264
55296 8.4 2.51 0.210 0.170 0.286
2.1. Methodology 55297 7.2 2.80 0.261 0.194 0.324
55303 5.0 2.80 0.330 0.217 0.352
Stability curves are generally plotted in a log T −log ξ/T diagram 55333 2.2 0.75 0.168 0.114 0.168
(e.g. Krolik et al. 1981), where T is the gas temperature and ξ 55334 2.0 0.70 0.166 0.115 0.166
its ionization parameter2 . In this diagram, an equilibrium state 55450 2.0 0.55 0.129 0.087 0.129
where the slope of the curve is positive is thermally stable, while 55559 2.2 0.33 0.073 0.043 0.073
it is unstable if the slope is negative, and the gas is then expected 55565 2.5 0.34 0.070 0.040 0.070
to rapidly collapse into a different stable equilibrium state. 55593 3.0 0.27 0.052 0.029 0.055
As said in the introduction, we used the best fit SED 55594 4.9 0.27 0.034 0.018 0.041
obtained by Marcel et al. (2019) in the Jet-Emitting Disk 55601 6.6 3.33 0.033 0.019 0.044
model framework to compute the stability curves. These SED 55606 15.3 0.35 0.017 0.009 0.028
reproduce the RXTE/PCA data of GX 339-4 observed during 55607 15.6 0.37 0.017 0.009 0.029
its 2010-2011 outburst. The JED framework and the way the 55617 24.2 0.15 0.005 0.003 0.008
SED are computed are described in a series of papers (Ferreira 55646 40.1 0.03 0.0006 0.0004 0.001
et al. 2006; Marcel et al. 2018b,a) to which the reader is referred Table 1. MJD, transition radius and accretion rate of some of the best
for more details. We have also reported in Appendix A a few fit SED obtained by Marcel et al. (2019) to reproduce the RXTE/PCA
informations in this respect. To summarize, the JED framework observations of the 2010-2011outburst of GX 339-4. We have also re-
assumes the presence of a Jet Emiting Disk in the inner region of ported the corresponding luminosities between 1 and 1000 rydbergs and
between 1 and 100 keV as well as the bolometric luminosity. The Ed-
the accretion flow, for disk radii < Rtr , and a Standard Accretion dington luminosity LEdd = 8.7×1038 erg.s−1 assuming a black hole mass
Disk (SAD) beyond Rtr . The total SED is mainly characterized of 5.8 M . The distance of GX 339-4 is taken equal to 8 kpc.
by Rtr and the accretion rate Ṁ reaching the inner compact
object. The high energy emission (above 1-2 keV) is dominated
by the JED emission while below ∼1 keV it is dominated by
the emission of the standard accretion disk. Both JED and SAD
emissions depend on Rtr and Ṁ. The JED emission is generally
dominated by the Compton process, the seed photon field being
a mix of local bremsstrahlung and synchrotron emission and
non-local emission from the SAD (see Marcel et al. (2018a). A
few SED examples are detailed in Fig. A.2).
Marcel et al. (2019) show that Rtr and Ṁ, and consequently
the broad band JED-SAD SEDs, are quite well constrained all
along the outburst thanks to the RXTE/PCA data. We have re-
ported in Tab. 1 the parameters Rtr and Ṁ as well as the corre-
sponding bolometric and ionizing (i.e. between 1 and 1000 Ry-
dbergs) luminosities (in Eddington units) of a few best fit SEDs
at different MJD along the 2010-2011 outburst of GX 339-4. We
have reported in Fig. 1 the Hardness-Intensity Diagram (HID) of
this outburst with the position of the different observations re-
ported in Tab. 1. The corresponding SEDs are plotted in the left
part of Fig. 2 and will be discussed later. Fig. 1. HID of the 2010-2011 outburst of GX 339-4. The position of the
These SEDs are then used in cloudy 17.01 (last described observations reported in Tab. 1 are indicated with blue and black colors
and are labelled on the HID with their MJD. The black (resp. blue) MJD
in Ferland et al. 2013) to compute the corresponding stability
correspond to observations whose range of ionisation parameter consis-
curves all along the outburst. We adopted Solar abundances (as tent with Fe XXV and Fe XXVI ions is in an unstable (resp. stable) part
in Table 7.1 of cloudy documentation3 ), a typical disk wind den- of the photoionisation stability curves. We have distributed the MJD ob-
sity n = 1012 cm−3 (see next Sect. 2.2 for a discussion on the servations in terms of modeled SED and associated stability curves in
effect of the density), a turbulence velocity vturb = 500 km s−1 Fig. 2.
and a column density log(NH /cm−2 ) = 23.5, as in Bianchi et al.
(2017).
2.2. Caveats
2
We use here the original Tarter et al. (1969) definition of the ionisa- While the SED have strong impact on the stability curves, other
tion parameter ξ = L/nr2 , where L is the total luminosity in ionizing parameters can also affect the heating/cooling equilibrium and
photons, n is the hydrogen density and r is the distance of the gas from modify the stability curve shape. For instance, Bianchi et al.
the illuminating source. (2017) looked at the effect of the chemical abundances and they
3
The cloudy document can be found at this link are marginal. Chakravorty et al. (2013) and Bianchi et al. (2017)
Article number, page 3 of 14
A&A proofs: manuscript no. 39524newb
looked at the effect of the plasma density and only high densi- (in soft and soft-intermediate states) have highlighted areas on
ties (above 1016 cm−3 ) have significant impact on the stability stable branches. This is in agreement with recent studies (e.g.
curve shape. In the case of hard state SED the slope of the sta- Chakravorty et al. 2013, 2016; Bianchi et al. 2017) and, as dis-
bility curves can even change and the branch consistent with Fe cussed in the introduction, this would explain the non observa-
XXV and Fe XXVI ions can move from thermally unstable to tions of Fe XXV-Fe XXVI absorption lines in hard states while
thermally stable conditions (see Fig. 5 of Bianchi et al. 2017). a wind could be still present.
Such high densities are however not consistent with the (admit- The daily observations of the 2010-2011 outburst of GX 339-
tedly rare) observational constraints (e.g. Kallman et al. 2009; 4 and the best fit SEDs obtained with the JED model allow us to
Schulz et al. 2008) nor expected from disk wind models in XrB follow the evolution of the stability curves all along the outburst.
(e.g. Chakravorty et al. 2016, Higginbottom et al. 2017). Our We describe below this evolution during the different spectral
choice of a wind density of n = 1012 cm−3 in our simulations stages of the source. While not unique, we follow the spectral
is then coherent with the fact that stability curves do not change state definitions of Marcel et al. (2019).
drastically for a wind density varying between 108 − 1016 cm−3
(see Chakravorty et al. 2013; Bianchi et al. 2017, and see also
Appendix B). 3.1. Hard state: from MJD 55208 to MJD 55293
The Cloudy code also assumes an isolated and static plasma
The first RXTE observation starts at MJD 55208 when the source
which is obviously not the case for a large scale wind. The effects
was already in a quite bright (L ' 2%LEdd ) hard state. GX
like thermal conduction or adiabatic coolings are thus not taken
339-4 stayed in the hard state until around MJD 55293 when
into account in our computation. Numerical simulations of ther-
it started transitioning to the soft state. The 1-1000 Ry luminos-
mal disk winds indicate however that thermal conduction should
ity increases by a factor 5-6 during this period (see Tab. 1). The
have a small effect on the heating/cooling equilibrium (e.g. Hig-
three best-fit SEDs obtained with the JED model for MJD 55208,
ginbottom et al. (2017) for thermal winds). Concerning adiabatic
55271 and 55293 are reported in Fig. 2a and the corresponding
coolings, they can also be neglected as long as the time to reach
stability curves in Fig. 2b. The SEDs are typical of hard states,
photoionisation equilibrium is, locally, shorter than the dynam-
dominated by a hard X-ray cut-off power law above ∼1-2 keV
ical timescale of the wind. While the observed line widths gen-
(produced by the inner JED) and a weak disk black-body com-
erally imply that the gas is supersonic, such conditions are actu-
ponent below, produced by the outer SAD. The power-law slope
ally verified in MHD disk wind solutions like those discussed by
appears roughly constant around 1.4-1.5 and the cut-off energy
Chakravorty et al. (2016). Actually, even if the plasma wind ve-
decreases when the luminosity increases. The disk black body
locity could be supersonic, its dynamical timescale (see an esti-
emission increases in flux and temperature in agreement with
mate given by Gonçalves et al. (2007) in their Eq. 8), is expected
the decrease of the transition radius Rtr between the JED and the
to be significantly longer than the other timescales involved in
SAD while the accretion rate increases (see Tab. 1).
the radiative equilibrium computation (e.g. ionisation time, re-
combination time, thermal time, see Gonçalves et al. (2007)). The computed stability curves are quite similar for the three
While these arguments suggest that the shape of the stability MJD 55208, 55271 and 55293. In the three cases, the tempera-
curves discussed in this paper should not strongly depend on our ture range that agrees with the right ionization range for Fe XXV
physical and numerical assumptions, a precise estimates would and Fe XXVI is unstable. Actually, if the wind exists during this
require a detailed modeling of the disk wind physical properties period, its temperature has to be in one of the ranges where the
and dynamics like in the recent work by Dannen et al. (2020); stability curves have a positive slope i.e. either at very high tem-
Waters et al. (2021) in the case of thermal disk winds. While perature (> 3 × 107 K) or in localized regions around 106 K,
this is an important step that should be done also in the case 2 × 105 K or at lower temperature < 3 × 104 K. In these temper-
of magnetically driven disk winds, this is however out of the ature ranges, the wind would not produce any Fe XXV and Fe
scope of the present paper. Some caution is nevertheless required XXVI absorption lines (see Sec. 3.7).
and our results must then be understood with these limitations in
mind. 3.2. Hard-to-soft transition: from MJD 55294 to MJD 55333
From MJD 55294 the source starts the transition to the soft state,
3. Stability curve evolution i.e. the path in the HID turns to the left. This transition lasts about
40 days, between MJD 55294 to around MJD 55333. During this
The stability curves corresponding to the MJD reported in Tab.
period the SEDs still show a power law component in the X-rays
1 are plotted in the right panels of Fig. 2 in the log T -log ξ/T
but the slope increases from ∼1.5 to 2.2 and the high energy cut-
plane. In this plane, the parts of the stability curves with positive
off decreases all along the transition (see Fig. 2c). On the other
(resp. negative) slopes are thermally stable (resp. unstable). The
hand, the disk component increases in flux and temperature. At
highlighted areas on each curve correspond to the range of ion-
MJD 55333, at the end of the transition, the SED is only domi-
isation parameter consistent with Fe XXV and Fe XXVI ions4
nated by the disk component.
and which can go from ∼ 103 to ∼ 106 erg s−1 cm depending
on the SED. They are colored in gray (resp. blue) if they are We have reported the corresponding stability curves in
located on an unstable (resp. stable) part of the stability curve. Fig. 2d. During this hard-to-soft transition, the stability curves
Clearly, the gray colored ones correspond to the observations on change drastically and at the end of the transition (after MJD
the right part of the HID, i.e. from MJD 55208 to 55295 and from 55296), the stability curves become thermally stable in almost
MJD 55594 to 55646, which are either hard or hard-intermediate all the temperature range used in the CLOUDY computations5 .
states of the outburst. On the contrary, all the other observations This includes the ionization range compatible with Fe XXV and
Fe XXVI ions.
4
More precisely, they correspond to a width in log ξ at 90 per cent of
5
the peak of their ionic fractions fion , fion (ξ) depending on the SED. We except in a narrow interval around 3 × 104 − 105 K, a temperature
have reported a few examples of ion fraction in the Appendix Fig. C.1. range which is irrelevant (because too low) for Fe XXV and Fe XXVI
Article number, page 4 of 14
P.-O. Petrucci et al.: Expected disk wind properties evolution along an X-ray Binary outburst
a) b)
c) d)
e) f)
g) h)
Fig. 2. SED (left) and corresponding photoionisation stability curves (right) between MJD 55208 and 55293 (hard state, a) and b)), MJD 55294
and 55303 (hard-to-soft transition, c) and d)), MJD 55304 and 55592 (soft state, e) and f)) and MJD 55593 and 55606 (soft-to-hard transition, g)
and h)). The stability curves are labeled with their corresponding MJD. The highlighted (blue and gray) areas on each curve correspond to the
range of ionisation parameter consistent with Fe XXV and Fe XXVI. They are colored in blue (resp. gray) if they are located on a stable (resp.
unstable) part of the stability curve.
Article number, page 5 of 14
A&A proofs: manuscript no. 39524newb
i) j)
Fig. 2. cont. i) Photoionisation stability curves and j) corresponding SED between MJD 55607 and 55646 (hard-to-quiescent state).
This change occurs in a couple of days (between MJD 55295 are also similar to those before the hard-to-soft transition (see
and MJD 55297) while the changes of the SED are quite minor. Sect. 3.1).
Within a day, from MJD 55295 to MJD 55296, the wind becomes
able to produce Fe XXV and Fe XXVI absorption lines. While
the bolometric luminosity varies by only a factor 1.4 during the 3.5. Hard-to-quiescence: from MJD 55607 to MJD 55646.
transition, with a maximum around MJD 55303, the ionizing lu- After MJD 55607, GX 339-4 is back to the hard state until the
minosity varies by a significantly larger factor ∼3.3 due to the end of the outburst. The bolometric luminosity decreases by
increase of the disk flux which dominates the 1-1000 Ry energy more than a factor 30 during this period. The lower the lumi-
range. nosity the more bumpy the SED shape (see Fig. 2i). This is char-
acteristic of the Compton process in a hot but tenuous plasma
where each scattering order produces well separated spectral
3.3. Soft state: from MJD 55334 to MJD 55559. bumps.
In the soft state, which lasts here about 225 days, the SED are We reported the corresponding stability curves in Fig. 2j.
mainly characterized by a disk component in this state (see Fig. They are typical of Hard State ones (see Sect. 3.1) and no Fe
2e). The stability curves are very similar to one another during XXV and Fe XXVI absorption lines are expected. The global
this entire state (see Fig. 2f) while the 1-1000 Ry luminosity de- shape of the stability curves seems to stiffen however when the
creases by a factor 4-5. The ionization range compatible with Fe source flux decreases, the “S” shape evolving to a “step” func-
XXV and Fe XXVI ions is always in a stable part of the stabil- tion where the upper hot and tenuous branch takes up the large
ity curves, meaning that the associated absorption lines can be part of the ξ/T range.
present. The presence of a hard tail can however significantly
impact the thermal equilibrium of the wind (see Sect. 3.6 and 3.6. Hard tail
Fig. 3).
The soft states can also present a low luminosity and steep power
law at high energy (above ∼ 10 keV), the so-called hard tail,
3.4. Soft-to-hard: from MJD 55561 to MJD 55606. whose origin is currently unknown (Remillard & McClintock
2006). It is generally badly constrained due to the lack of statis-
At MJD 55559, the path of GX 339-4 starts to turn right in the tics, reaching up to a 50% error on the photon index for example.
HID, the source transiting back to the hard state. This transition Marcel et al. (2019) includes this hard tail in the SED by adding
lasts about 40 days until around MJD 55606. We have reported a power-law component to the synthetic spectra each time the
a few best fit SEDs during this transition in Fig. 2g. The disk fitting procedure favors a pure blackbody emission (see Marcel
component decreases in flux and temperature while the X-ray et al. (2018a) for a detailed discussion). The photon index of this
power law hardens and the high-energy cut-off increases. The 1- power-law component is set to Γ = 2.5 and it is normalized in
1000 Ry and bolometric luminosities decrease by a factor ∼2.2 order to contribute to a fixed fraction of the 2-20 keV energy
and ∼2.6 respectively during this transition. range (typically between 1% and 20%, Remillard & McClin-
We reported the corresponding stability curves in Fig. 2h. tock 2006). We report in the left of Fig. 3 the stability curves
Like in the hard-to-soft transition, the shape of the stability for MJD 55410 assuming different hard tails with different flux
curves changes drastically during the soft-to-hard transition. (contributing to 1 and 20% of the 2-20 keV flux) but with a fixed
Moreover, and again similar to the hard-to-soft transition, the photon index (Γ=2.5). In the right panel, we assume hard tails
change from stable to unstable conditions for the ionization with different spectral indices (Γ=2.5 and 2) but a constant flux
range compatible with Fe XXV and Fe XXVI ions occurs in a (contributing to 10% of the 2-20 keV flux). These different ex-
couple of days. While at MJD 55592 the stability curve is similar amples show that the presence of this hard tail can have some
to that of soft states, at MJD 55594 it becomes the same as hard effects on the stability curves but is not sufficient to change a
states at the beginning of the outburst. Moreover, the tempera- soft state-like into a hard state-like shape. Moreover its impact
ture ranges of thermal stability after the soft-to-hard transition on the thermal stability of the hot wind in the soft state should
Article number, page 6 of 14
P.-O. Petrucci et al.: Expected disk wind properties evolution along an X-ray Binary outburst
Fig. 3. Effect of the hard tail on the photoionisation stability curves. Application to MJD 55410. Left: hard tails with constant photon indexes
Γ=2.5 but with different fluxes contributing to 1 and 20% of the 2-20 keV flux. Right: hard tails with different photon index (Γ =2 and 2.5) but a
constant flux contributing to 10% of the 2-20 keV flux.
not drastically change the existence of a stable ionisation domain range of ionisation parameters is always thermally stable in the
for Fe XXV and Fe XXVI. soft state. Moreover, the observations of hot wind signatures in
soft states indicate that the wind properties agree with this stable
range of ionisation. Assuming that a wind is always present dur-
3.7. Low temperature phases
ing the entire outburst, as we did in this work, we wonder then
All the stability curves plotted on Fig. 2 and 3 show low tem- how the wind properties should evolve during the state transition
perature domains (around 104.5 and 105 K) which are thermally while reaching (in the case of the hard-to-soft transition) or leav-
stables. If part of the wind plasma is in this range of tempera- ing (in the case of the soft-to-hard transition) the soft state ionisa-
tures, absorption lines from low ionisation-level ions could also tion conditions. Some interesting constraints need to be satisfied
be observable. Of course this will strongly depend on the total as discussed below. As noticed in Sect. 2.2 however, it is worth
column density of this low temperature plasma on the line of keeping in mind that the true evolution of the plasma would re-
sight. For instance, in the case of the transient accreting neu- quire detailed modeling of the disk wind physical properties and
tron star AX J1745.6-2901, Bianchi et al. (2017) tested the case dynamics (e.g. Dannen et al. 2020; Waters et al. 2021). While
where the column density is equal to the one deduced from the out of the scope of the present paper, they could significantly
Fe XXV and Fe XXVI absorption lines. This low temperature affect the following comments.
phase, if present on the line of sight, would then block all the
radiation in the soft X-rays. On the other hand, Bianchi et al.
4.1. Changes in the disk wind properties during spectral
(2017) estimate the filling factor of this phase to be very low.
transitions
So this strong absorption would only be observed as a sporadic
change of the persistent neutral absorption and, in the case of 4.1.1. From Hard-to-soft
AX J1745.6-2901, this was tentatively associated to the dips ob-
served in this source Bianchi et al. (2017). We simulated with As shown in Sect. 3, only a few temperature domains are
Cloudy cases with lower column densities where the absorption thermally stable during hard states (see Fig. 2b) either at very
is less severe. No absorption lines are present above 1 keV, but high temperature (> 3 × 107 K) or in localized region around 106
some significant absorption is observed below 1 keV and strong K, 2 × 105 K or at low temperature < 3 × 104 K. As already said,
absorption in the UV down to the IR. Note also that the ionisa- the ionization range compatible with Fe XXV and Fe XXVI
tion parameter is quite low in these phases (< 103 ). This could is itself thermally unstable. In the soft state however, a large
correspond to unphysical large distance from the black hole. In part of the temperature domain is thermally stable including
other words, these low temperature phases may simply not exist the ionization range compatible with Fe XXV and Fe XXVI.
for compact systems. In order to become detectable at the end of the Hard-to-Soft
transition, the hot wind properties cannot be casual at the
beginning. They have to evolve from the stable temperature
4. Discussion domains of the hard states to the “hot wind" domains of the soft
We use the best fit SED obtained by Marcel et al. (2019) to com- states.
pute the stability curves presented in Sec. 3. These SED have
been computed in the JED-SAD framework and reproduce the Interestingly, this evolution is unlikely to occur at constant
spectral evolution of GX 339-4 during its 2010-2011 outburst. wind density distribution (i.e. constant nr2 ) as shown in Fig. 4.
We show that the range of ionisation parameters consistent with This figure is similar to Fig. 2d but we over-plotted two different
Fe XXV and Fe XXVI ions is always in a thermally unstable paths (square/dashed line; star/dashed line) which correspond to
part of the stability curves in the hard state. On the contrary, this two different wind evolutions at constant nr2 . The square/dashed
Article number, page 7 of 14
A&A proofs: manuscript no. 39524newb
line starts from the stable part of the temperature domain of the
hard state around 106 K (indicated by a square on the stability
curve of MJD 55294). During the spectral evolution between
MJD 55294 and MJD 55333, this path always stays on a stable
part of the stability curves but it never crosses the “hot wind”
domain of the soft states. In consequence, no signature of a hot
wind will be visible in the soft states at the end of the transition.
The same conclusion is obtained if the wind is initially (during
MJD 55294) on one of the stable branches existing at lower
temperature (< 106 K).
The other path (star/dashed line) starts from the top hot sta-
ble branch (T > 3×107 K) of the hard state, at the very beginning
of this temperature domain (indicated by a black star on the sta-
bility curve of MJD 55294). During the spectral evolution of the
system, this path crosses the stable “hot wind" domains of the
soft states only after MJD 55297. Actually only the constant nr2
paths that start in the small temperature domain underlined in red
on the stability curve of MJD 55294 will cross the “hot wind” do-
Fig. 4. The colored lines are the photoionisation stability curves dur-
main of one of the soft states at the end of the transition. Indeed, ing the Hard-to-Soft transition (see Fig. 2 for the meaning of the
a plasma at a temperature just below the red segment is unstable. blue and gray segments). The black dashed lines (squares/dashed line;
And for a plasma at a temperature larger than the red segment, star/dashed line) correspond to different paths with constant nr2 . The
constant nr2 paths will never cross a “hot wind" domain of the red lines are the paths followed by the wind assuming an increase (for
soft states and no wind will be detected at the end of the tran- the red dotted path) or decrease (for the red dashed path) of the wind
sition. This red segment corresponds however to a very limited density by a factor 3 between MJD 55295 and MJD 55296. See Sect.
range of temperature and ionisation parameter in the hard state. 4.1.1 for the small temperature domain underlined in red on the stability
To reach the soft state, it appears more reasonable to assume a curve of MJD 55294. The arrows indicate the time evolution.
change in the wind physical characteristics during the transition
(i.e. nr2 does not stay constant). As an example, we over-plotted
in red dashed lines the paths followed by the wind if its density
increases (red star/dashed line) or decreases (red square/dashed
line) by a factor 3 between MJD 55295 and MJD 55296. In both
cases, the change in density modifies significantly the paths com-
pared to the constant nr2 cases and they now cross the “hot wind”
domains during almost all the soft state. Although empirical, this
strongly supports the need for a change in the wind properties
during the Hard-to-Soft transition in order to have detectable Fe
XXV and Fe XXVI lines in the soft states. Actually the minimal
increase of density to reach a stable "hot wind" domain when
coming from the black star/dashed line path is of about 30%
while the minimal decrease of density when coming from the
black square/dashed line path is of about a factor 2.
4.1.2. From Soft-to-Hard
We can repeat a similar procedure to follow the evolution of
the wind thermal state during the transition from the soft to the
Fig. 5. The colored lines are the photoionisation stability curves dur-
hard state. This is illustrated now in Fig. 5. Let us assume that
ing the Soft-to-Hard transition (see Fig. 2 for the meaning of the blue
at the beginning of the transition the wind is in the conditions and gray segments). The black stars/dashed line correspond to a path of
where Fe XXV and Fe XXVI lines are detectable (black star constant nr2 from MJD 55565 until MJD 55594. The vertical red dotted
on the MJD 55593 stability curve). Then a path at constant nr2 lines correspond to isobaric (constant ξ/T ) evolutions of the wind. The
(black dashed line) reaches the unstable temperature domain black square/dashed lines correspond to path of constant nr2 starting
of the stability curve of MJD 55594 (black star on the MJD from MJD 55594. The arrows indicate the time evolution.
55594 stability curve). Actually, looking at the shape of the
stability curves, this evolution does not depend strongly on the
starting point in the “hot wind” domain of the soft states (MJD a change of the wind temperature and density. Locally, as soon
< 55594), and, as long as nr2 stays constant, the wind will as the plasma reaches a new (stable) temperature, the new ion-
inevitably reach an unstable state when the X-ray source enters ization equilibrium is expected to settle in almost immediately
in the hard state at MJD 55594. (Gonçalves et al. 2007). Of course, the complete migration of the
gas from a thermally unstable to a thermally stable state, which
The evolution of the wind after MJD 55294 is thus quite un- is itself a mix of hot and cold phases in interaction, will take
known. The thermal instability forces the wind plasma to leave some time. This is expected to occur on a time scale tmigr of the
the thermally unstable temperature domain and to reach the other order of ∆H/c s where ∆H is the thickness of the thermally un-
stable branches of the stability curve. This necessarily requires stable region and c s is the sound velocity in the cold phase (see
Article number, page 8 of 14
P.-O. Petrucci et al.: Expected disk wind properties evolution along an X-ray Binary outburst
discussion in Gonçalves et al. 2007). This translates to: reason why the slow time evolution of the far-out wind driving
zone should always be contemporaneous with the rapid spectral
N23 changes of the SED emitted from the innermost disk regions.
tmigr . 2 × 104 1/2
(in units of s) (1)
T 5 n12 Irradiation of the outer disk by the inner X-ray emission seems
the most natural process to link these two very distant regions
where N23 is the column density in units of 1023 cm−2 , n12 on a very short timescale. Such a radiative feedback of the inner
is the hydrogen density in units of 1012 cm−3 and T 5 is the regions on the outer disk wind properties is plausible, since the
temperature of the cold gas in units of 105 K . Assuming a deposition of any additional power Q at the disk surface leads to
maximal extension of the disk wind of the order of the binary the enhancement of mass loss, both in magnetically-driven (e.g.
separation in GX 339-4, i.e. ∼ 1012 cm (Zdziarski et al. 2004, Casse & Ferreira 2000) and thermally-driven (e.g. Higginbottom
2019), and an optically thin wind, tmigr is shorter than a day. & Proga 2015) outflows.
So the migration can easily occur between two RXTE pointings
(generally separated by 1 day). The amount of X-ray luminosity incident on the disk at a
radius r = R/Rg in a ring of thickness ∆r will depend on the exact
The vertical dotted segments in Fig. 5 indicate the cases geometry. Estimates from simple radial profile of the disk aspect
where the evolution of the gas after MJD 55594 occurs at con- ratio provide a too low X-ray irradiation which does not fit with
stant pressure (isobaric evolution i.e. a constant ξ/T ) and fast the required disk accretion transport to explain the XrB outburst
enough to assume that the average distance of the gas to the X- light curve durations (e.g. Dubus et al. 2001; Tetarenko et al.
ray source would not change. In this case, the wind plasma can 2018a, 2020). Following Dubus et al. (2001), the intercepted and
transition to two different stable solutions, one hotter and the reprocessed X-ray irradiation (which corresponds to the heating
other colder, indicated by the upper and lower red squares re- power deposit Q we are looking for) by a disk ring can be simply
spectively on the MJD 55594 stability curve. It is also possible expressed as:
that the wind evolves into a mix of these two different plasma
phases where colder (and denser) structures are embedded in a LX ∆r
Q ' Cirr 2
2πrdr = Cirr LX (2)
hotter (less dense) gas. This situation would be very similar to 4πr 2r
the one discussed by Bianchi et al. (2017) in the case of the wind
with Cirr a parameter which encapsulates our ignorance concern-
evolution observed in the neutron star AX J1745.6-2901 between
ing the irradiation geometry, the X-ray albedo and X-ray irradi-
its soft and hard state. After MJD 55594, each of the two possi-
ating spectral shape. Cirr is estimated to be ' 0.05 to explain the
ble wind phases will keep on evolving depending on the spectral
XrB outburst light curve durations (see ? and references therein).
evolution of the X-ray source. As examples, we over-plotted in
Actually, a (weak) radial dependence of Cirr is expected due to
Fig. 5 in red dashed lines the two possible paths where nr2 is
the radial variation of the disk aspect ratio (see Dubus et al.
assumed to be constant.
2019 and references therein). The scattering of the X-rays by
the disk wind itself can also have some impact on the disk irra-
4.1.3. A very favorable configuration for disk wind detection diation (Dubus et al. 2019; Kimura & Done 2019). But for the
present discussion we will assume Cirr to be constant equal to
Interestingly, during the soft-to-hard and hard-to-soft transitions, 0.05. Equation 2 then shows that the heating through irradiation
the shape of the stability curve becomes almost vertical in the is directly related to the X-ray luminosity. The thermal timescale
ionization range compatible with Fe XXV and Fe XXVI ions on which the disk matter is heated is given by (e.g. Gonçalves
(see e.g. the stability curve of MJD 55296 in Fig. 2h). This cor- et al. 2007):
responds to a situation where pressure equilibrium is satisfied in
this ionisation domain and this is a quite favorable mechanical T5
configuration for the wind. This could explain why we generally tth ∼ sec. (3)
n12 Λ23
observe the strongest wind absorption features in the middle of
the transition states (see Ponti et al. 2012). where, like in Eq. 1, n12 is the density expressed in 1012 cm−3 ,
T 5 is the temperature in 105 K and Λ23 is the cooling function in
10−23 erg cm3 s−1 . It is thus reasonable to expect thermalization
4.2. Disk irradiation as a potential driver of the change of the
time scales of seconds to minutes. The travel time for the X-ray
disk wind properties during the hard-to-soft transition
photons produced at a few Rg from the black hole to reach
As shown in Sect. 4.1.1, if we want to observe a hot wind at the the outer disk (R > 104 Rg ) is of the same order of magnitude.
end of the hard-to-soft transition, an increase (or a decrease de- Finally the density adjustment of the wind will follow the
pending on the wind phase at the beginning of the transition) of thermal adjustment of the underlying disk on, typically, the
the wind density seems to be needed to make the wind evolving local keplerian time scale which is less than a day even at a disk
into the stable ionization range for Fe XXV and Fe XXVI ions. radius of 105 Rg (assuming a 10 solar mass black hole). Overall
It is hard to estimate the timescale for such evolution given the entire process (irradiation and wind density adjustment) is
the lack of long (several days) and continuous monitoring expected to occur in less than a day.
of a hard-to-soft state transition of an XrB. But the fact that
absorption features are regularly observed in soft states suggests We have reported the X-ray luminosity LX computed from
that the wind properties should evolve rapidly (on ∼ days) the SED between 1 and 100 keV in Tab. 1. The luminosity LX
after its entry in the soft state. This is somewhat problematic if increases rapidly at the beginning of the transition with an in-
the wind density scales only with the local disk density. Since crease of a factor ∼1.5-2 between MJD 55294 and MJD 55303
the latter scales with the disk accretion rate, the wind density while the accretion rate stays roughly constant (see Tab. 1). Our
would be expected to increase and then decrease during the qualitative estimates then suggest an increase of the disk surface
outbursting cycle. However, the disk wind region is estimated to heating through irradiation by the inner X-ray source during the
be located quite far away, beyond 104 Rg . There is therefore no hard-to-soft transition and, consequently, a potential increase of
Article number, page 9 of 14
A&A proofs: manuscript no. 39524newb
the disk wind mass loading and wind density in a short (less than would correspond to our JED, powerful jets are rather produced
a day) timescale. Thus, looking at Fig. 4, our result supports the (e.g. Liska et al. 2020). Our results thus provide a case for the
scenario with an increase of the wind density during the tran- presence, in XRBs, of a large scale magnetic field throughout
sition. A more quantitative impact on the wind density would the entire accretion disks and whose magnetization would evolve
require however a precise modeling of the thermal balance of from high values in the inner regions (i.e. Liska et al. (2020)
the disk outflowing disk surface layers which is out of the scope configuration), to much lower values in the outer regions, where
of the present paper. a disk wind would be launched (i.e Zhu & Stone (2018) or
Jacquemin-Ide et al. (2019) configuration). In recent 3D simu-
lations (Jacquemin-Ide et al. 2020), such a radial stratification of
5. Concluding remarks the magnetization is expected as the outcome of a global read-
We studied the expected evolution of the thermal properties of a justment of the disk (see also Scepi et al. 2019, 2020). If true,
hot disk wind (e.g. characterized by the presence of absorption this could have a significant impact on the secular evolution of
lines of Fe XXV and Fe XXVI ions) in a low-mass X-ray binary the accretion flow.
assuming it is present during the entire outburst (e.g. Sánchez- Acknowledgements. Part of this work has been done thanks to the financial sup-
Sierras & Muñoz-Darias 2020). For that purpose we have used ports from CNES and the French PNHE. SBi acknowledges financial support
from the Italian Space Agency under grant ASI-INAF 2017-14-H.O. GP ac-
the best fit SEDs obtained by Marcel et al. (2019) to reproduce knowledges funding from the European Research Council (ERC) under the Eu-
the RXTE/PCA data of GX 339-4 during the 2010-2011 outburst ropean Union’s Horizon 2020 research and innovation program (grant agreement
of the source. These broad-band SEDs have been obtained in the No. [865637]).
Jet Emitting Disk framework described in Ferreira et al. (2006);
Marcel et al. (2018a,b). For each of the 274 SEDs, we com-
puted the corresponding stability curve using the CLOUDY soft-
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